台灣淘米論壇's Archiver

22058153 發表於 2019-3-21 17:40

【數學】不定積分

[attach]1823505[/attach]

[attach]1823506[/attach]

求15題的計算過程,答案是最下面的。

22169751 發表於 2019-3-21 20:02

[img]https://latex.codecogs.com/gif.latex?\int&space;ln(x^{2}+9)dx[/img]
[img]https://latex.codecogs.com/gif.latex?=xln(x^{2}+9)-\int x\frac{2x}{x^{2}+9}dx[/img]
[img]https://latex.codecogs.com/gif.latex?=xln(x^{2}+9)-\int&space;\frac{2x^{2}+18-18}{x^{2}+9}dx[/img]
[img]https://latex.codecogs.com/gif.latex?=xln(x^{2}+9)-\int&space;2dx+18\int&space;\frac{1}{x^{2}+9}dx[/img]
令x=3tanθ dx=3sec²θdθ
[img]https://latex.codecogs.com/gif.latex?=xln(x^{2}+9)-\int&space;2dx+18\int&space;\frac{3sec^{2}\theta&space;}{9sec^{2}\theta&space;}d\theta[/img]
[img]https://latex.codecogs.com/gif.latex?=xln(x^{2}+9)-\int&space;2dx+6\int&space;d\theta[/img]
[img]https://latex.codecogs.com/gif.latex?=xln(x^{2}+9)-2x+6tan^{-1}\frac{x}{3}+c[/img]

22058153 發表於 2019-3-21 20:28

謝謝你!我懂了

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